JEE Mains · Maths · STD 11 - 10.1 circle and system of circle
The number of common tangents, to the circles \(x^2+y^2-18 x-15 y+131=0\) and \(x^2+y^2-6 x-6 y-7=0\), is :
- A \(3\)
- B \(2\)
- C \(1\)
- D \(4\)
Answer & Solution
Correct Answer
(A) \(3\)
Step-by-step Solution
Detailed explanation
\(C_1\left(9, \frac{15}{2}\right) \quad r_1=\sqrt{81+\frac{225}{4}-131}=\frac{5}{2}\) \(C_2(3,3) r _2=5\) \(C_1 C_2=\sqrt{6^2+\frac{81}{4}}=\frac{15}{2}\) \(r _1+ r _2=\frac{15}{2}\) \(C _1 C _2= r _1+ r _2\) Number of common tangents \(=3\)
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